Problem: Simplify the following expression: $p = \dfrac{-54n + 48}{42n + 60}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-54n + 48 = - (2\cdot3\cdot3\cdot3 \cdot n) + (2\cdot2\cdot2\cdot2\cdot3)$ The denominator can be factored: $42n + 60 = (2\cdot3\cdot7 \cdot n) + (2\cdot2\cdot3\cdot5)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $p = \dfrac{(6)(-9n + 8)}{(6)(7n + 10)}$ Dividing both the numerator and denominator by $6$ gives: $p = \dfrac{-9n + 8}{7n + 10}$